The perimeter of the rectangle is 54 cm. Its length is 2 times its width. What is the area of the rectangle?

Let the length of the rectangle be X cm and its width equal to Y cm.

Then the perimeter of the rectangle is: P = 2 * (X + Y) = 54 cm.

(X + Y) = 54/2 = 27 cm. (1)

By condition, X = 2 * Y. (2).

Let us solve the system of equations by the substitution method.

Substitute Equation 2 into Equation 1.

2 * Y + Y = 27.

3 * Y = 27.

Y = 27/3 = 9 cm.

X = 2 * 9 = 18 cm.

Determine the area of the rectangle.

S = X * Y = 18 * 9 = 162 cm2.

Answer: The area of the rectangle is 162 cm2.